Relations and Functions Flashcard

Front

What is a function?

Back

A function is a relation in which each input (x-value) is associated with exactly one output (y-value).

Front

How can you determine if a set of ordered pairs is a function?

Back

A set of ordered pairs is a function if no two pairs have the same first element (input) with different second elements (outputs).

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

Front

What does a mapping diagram show?

Back

A mapping diagram visually represents the relationship between inputs and outputs, showing how each input is paired with an output.

Front

What is the definition of a relation?

Back

A relation is a set of ordered pairs, which can include functions but does not have to.

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, as long as each input is associated with only one output.

Front

What is an example of a function?

Back

An example of a function is the set of ordered pairs {(1,2), (2,3), (3,4)}.

Front

What is an example of a relation that is not a function?

Back

An example of a relation that is not a function is the set of ordered pairs {(1,2), (1,3), (2,4)}.

Front

What is the significance of the x-value in a function?

Back

The x-value (input) is significant because it determines the corresponding y-value (output) in a function.

Front

What does it mean for a function to be one-to-one?

Back

A one-to-one function is a function where each output is associated with exactly one input, meaning no two different inputs produce the same output.